SOLUTION: Solve: x^3-2x ≤ 24

SOLUTION: Solve: x^3-2x ≤ 24 - 5x^2

Question 373566: Solve:
x^3-2x ≤ 24 - 5x^2
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
x^3-2x - 24 + 5x^2 ≤ 0

let study the roots of : x^3 + 5x^2 -2x - 24 = 0

Guess x=2 : 8 + 20 - 4 - 24 =0, 2 is a root, hence we can expand in terms like P(x)*(x-2)

x^3 - 2x^2 + 7x^2 - 14x + 12x - 24

=x^2(x-2) +7x(x-2) + 12(x-2)

=(x-2)(x^2 + 7x + 12)

=(x-2)(x+3)(x+4)

hence the two curves cross at 2, -3, -4

the inequality holds when the polynomial is negative, hence for

Solution if : x<-4 and x in [-3;2]

solution if green curve is greater than the red one :

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SOLUTION: Solve: x^3-2x &#8804; 24 - 5x^2

SOLUTION: Solve: x^3-2x ≤ 24 - 5x^2